In chapter 4, the crowds had been growing around Jesus and His teachings. By the opening of chapter 5, He is addressing a crowd that has followed Him there. He goes up to the mount and delivers the first of His recorded sermons.
It opens with the Beatitudes, which are often quoted in all kinds of places:

3“Blessed are the poor in spirit, for theirs is the kingdom of heaven.

10“Blessed are those who are persecuted for righteousness’ sake, for theirs is the kingdom of heaven.

11“Blessed are you when others revile you and persecute you and utter all kinds of evil against you falsely on my account.12Rejoice and be glad, for your reward is great in heaven, for so they persecuted the prophets who were before you.

I had never really thought about it before, but these are a kind of greeting and acknowledgement of the group that is following Him. He’s recognizing that it is the poor in spirit, those who mourn, the meek, the hungry and thirsty, the merciful, the pure in heart, the peacemakers, and those who are or will be persecuted for Jesus that are following Him at this point. It’s the people who need healing and their friends or family who brought them to the healer, and the people who His message speaks to. I feel like He’s telling these people that are following Him already that they’re going to be okay no matter what happens in this world after this because He’ll make it up to them later.
Then Jesus begins to unpack some other issues of the day. This is just my opinion, but issues with the Law and discrepancies with the way they are followed are issues of the day. If you recall in the times of the Kingdom of Israel, the times when the people were faithful and bring their problems to God are the times when their problems, like being ruled by Rome, are taken care of by God. So when he talks about the saltiness of the people and their light under a lamp, Jesus is talking about not being the example of faithfulness that brought fear into their hearts like in the time of Samuel and David.
The first message is about salt and light and Jesus telling them that they’re falling short of expectations. They aren’t being that example to the rest of the world the same way that they had been in times when no one else wanted to mess with them. God wasn’t with them because they weren’t with Him.
Jesus explains that He is not there “to abolish the Law or the Prophets”. It’s interesting because He says that and immediately begins to talk about the Law, quoting what they seem to know about it already and then amending it. But He really isn’t getting read of anything so much as explaining that there is more to what’s going on than action. The thoughts and words of people who are not outwardly breaking commandments are just as important to God when it comes to their righteousness.
It’s the kind of things that makes sense now and after He has come down and said it all so long ago, but I can see that being a bit of a revelation. At the same time, there have been many examples of Prophets telling the Israelites that their hearts and minds have to be behind their actions too. When the people were following other things God said to them in the Old Testament but not holding God as their only God or clearly just going through the motions, it never counted before. So, rather than just not committing adultery, you shouldn’t want to commit adultery if you are righteous. Sure, makes good sense.
From the feminist standpoint, I particularly appreciate that Jesus is not blaming the object of lust for anyone’s lust. Sure, He explains it in a gendered way, but He’s not saying that the woman a man lusts after is responsible, but his eye caused him to sin and it should be thrown out. That may sound pretty harsh and I’m not suggesting people gouge out their eyes, but it’s important that this is known. That person has a problem and not the object of his lust. The object of his lust hasn’t necessarily done anything to attract it and shouldn’t be blamed. Of course, this is again a gendered example, and I believe that has more to do with the language than this being a gendered issue. Women are just as capable of being lustful.
The statements on adultery aren’t exactly what a person wants to hear these days though. I did look up what was meant by “sexual immorality” in verse 32 and it is also translated as “adultery” quite often. If a woman is cheating, her husband can still leave her. The whole idea of a certificate of divorce is only mentioned once by Moses before this during his second speech in the middle of a miscellaneous set of laws. Other than that, divorce is mentioned as something that cannot happen at all when it is a marriage as a result of rape (reminder that this is so the woman or girl isn’t left destitute on account of not being a virgin and the man who raped her is responsible for her well-being for the rest of his life and not intended as an easy way to get a wife). In the original, the man can just write her the certificate for being “displeased somehow” and it did appear to be just the men that can do this as the household didn’t belong to the women and the men could not be kicked out of it.
I also find the amendment of “eye for an eye” interesting. I went back and referenced where that originally came from and that punishment was for the judges to put down, not for people to randomly obtain and only after more than one witness came forward against that person. This reinforces the idea that it is not any random person who can just retaliate or exact revenge for an actual or perceived slight. The Law must be consulted and the injustice verified. The amendment here goes beyond not trying to retaliate or get revenge and on to giving more than that person wants of you. It’s a concept that we have difficulty with so many centuries later.
Finally, Jesus asks His followers to love their enemies as well as their neighbors and gives an explanation of why He wants that. He’s asking them to go far beyond than that which is human nature, much like in the earlier sections. Don’t just act like a good person, think like one too. The sermon goes on in the next chapter and we’ll take a look next week at what that entails.
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Chapter links go to the ESV translations at Biblehub.com but I’m reading from the ESV Global Study Bible, which is available for free on the Kindle Reading App.